How to use for loops to calculate the determinant of the first n powers of 2x2 matrix (A) without using the implicit Matlab command "det"
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I am allowed to use the for loop as well as if/elseif/else statements to create the function but I am not sure how exactly to do this. The input will be a matrix A and a scalar value n. I began using if statements to make sure that the matrix is 2x2 and that n is positive however i do not know how to code for det(A^n) without using the det function. Below is an example of what i have thus far:
function ret = invertiblePowers(A,n)
if isequal(size(A), [2 2])==0
ret= disp('Matrix has wrong dimensions')
elseif floor(n)~=ceil(n)
ret= disp('n is not a positive integer')
elseif isequal(size(A), [2 2])==1 & floor(n)=ceil(n)
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WAT
2015-9-28
You're going to want a function that takes A and n as inputs and either returns a string or nothing at all. That would look like
function ret = invertiblePowers(A,n)
or
function [] = invertiblePowers(A,n)
Assuming you want to return a string, then just do something like
function ret = invertiblePowers(A,n)
ret = ''; % initialize ret to empty string
% Make sure A is the right size
if (~isequal(size(A),[2,2]))
ret = 'Matrix has wrong dimensions'; % note that 'disp' is not used
return; % stop working and exit out of this function
end
% Make sure n is positive integer
if ((floor(n)~=ceil(n)) || (n <=0))
ret = 'n is not a positive integer';
return;
end
% if A is 2x2 and n is positive integer, find det(A^n)
% It's unclear whether this function needs to find all
% determinates for I=1 up to n, or just n.
% Assuming you want 1:n, loop through
for i = 1:n
An = A^i; % raise A to the ith power
% find the determinate here, you need to do this part
detAn = YOUR MATH HERE;
% append results to return string
ret = [ret ; sprintf('n = %i : det(A^n) = %f',i,detAn)];
end % end for loop
end
更多回答(2 个)
Walter Roberson
2015-9-28
This together with the fact that with SVD, the N'th power of the matrix can be found by taking the N'th power of the diagonal.
Or you could just use the formula for the determinant of a 2 x 2 matrix.
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WAT
2015-9-28
I wouldn't assume you're allowed to use the rule that det(A^n) = det(A)^n. I'd assume you're supposed to calculate A^n then find the determinate of that new matrix.
James Tursa
2015-9-28
To calculate the determinant of a 2x2 matrix, see this link a little over halfway down the first page:
To get the determinant of a matrix power, det(A^n), also note from the above link that the determinant of a matrix product is the product of the individual determinants. I.e. det(A*A) = det(A)*det(A). So you can extend this to powers and figure out the formula for det(A^n).
Using the above hints should help you to write the code.
2 个评论
WAT
2015-9-28
I'm guessing that discovering that relationship between det(A^n) and det(A) is the point of this problem =P
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